Research on spatial patterns in geochemical data is an important theme with both theoretical and applied value. The analysis is relatively complicated because of the comprehensive interaction between diverse environmental factors such as geology, hydrology, landforms, and human activities. To make full use of these data by using multivariate statistical methods to model and estimate spatial pattern needs further research.
Approaches based on fuzzy set theory came out only in the mid-1970s when the theory was accepted fairly widely and algorithms became available. There are two kinds of fuzzy classification: the semantic import model (SI) and fuzzy k-means clustering (FKM) (Gaans, 1993). The employment of the SI model depends on the existence of a well defined and functional classification scheme. Conversely, the FKM approach is an unsupervised classification approach and does not need prior knowledge. Generally speaking, FKM, also known as FCM, is better developed and widely used in diverse disciplines.
The application of a continuous or fuzzy classification for geographical phenomena arose for the following reasons:
The results show that a combination of NLM and FKM provides a set of powerful tools to analyse the spatial pattern. The spatial variation of geochemical parameters primarily is influenced by lithology in the region.
Fuzzy concepts suit a reality which shows gradual variation both in the multivariate and geographical space. The two alternative methods, NLM and FKM, seem to be a natural couple for the analysis of fuzzy classification, and should be used more widely in geographical information handling and environmental studies.
Fuzzy approaches have drawn wide attention from geographers (Burrough, 1990). It seems necessary to integrate some mature fuzzy approach into GIS. Odeh et al. (1992) suggest that if the FKM method be integrated into GIS considerable benefits could be accrued. We think a loose coupling is a suitable way to accept new spatial analysis methods. In our research we use a loose interface between GIS and FKM and NLM algorithms by moving data files between them. In addition, there is a need for users to visualize the intermediate results and make judgements about the model and parameters which are needed to perform the analysis in the next step. This means the whole process has to be an interactive one. The results of FKM and NLM should be well displayed and represented in graphics and in text with respect to the need of users.
The author would like to thank Graeme Bonham-Carter of the Geological Survey of Canada for generously providing the geochemical data for northern Vancouver Island. Special thanks are due to Dr. Anthony C. Gatrell and Dr. Robin Flowerdew who gave me supervision through the research.